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A decagon is a 2-dimensional polygon with ten edges[1]. The Bowers acronym for a decagon is dec[2].

## Structure and Sections

The regular decagon has each angle at 144 degrees. It can be seen as a truncated pentagon.

### Subfacets

• Vertex radius: $\frac{1+\sqrt{5}}{2}l$
• Edge radius: $\frac{\sqrt{5+2\sqrt{5}}}{2}l$

### Angles

• Vertex angle: 144º

### Vertex coordinates

The vertices of a regular decagon of side 2 can be given by all changes of sign of:

• (1, √(5+2√5))
• ((3+√5)/2, √((5+√5)/2))
• (1+√5, 0)

### Related shapes

• Dual: Self-dual
• Conjugate: Decagram
• Vertex figure: Line segment, length $\sqrt{\frac{5++\sqrt{5}}{2}}$
• Third diagonal: Length $\frac{3+\sqrt{5}}{2}$
• Fourth diagonal: Length $\sqrt{5+2\sqrt{5}}$
• Long diagoal: Length $1+\sqrt{5}$

$\{0\}$ $\{1\}$ $\{2\}$ $\{3\}$ $\{4\}$ $\{5\}$ $\{\frac{5}{2}\}$ $\{6\}$ $\{7\}$ $\{\frac{7}{2}\}$ $\{\frac{7}{3}\}$ $\{8\}$ $\{\frac{8}{3}\}$ $\{9\}$ $\{\frac{9}{2}\}$ $\{\frac{9}{4}\}$ $\{10\}$ $\{\frac{10}{3}\}$ $\{11\}$ $\{\frac{11}{2}\}$ $\{\frac{11}{3}\}$ $\{\frac{11}{4}\}$ $\{\frac{11}{5}\}$ $\{12\}$ $\{\frac{12}{5}\}$ $\{13\}$ $\{\frac{13}{2}\}$ $\{\frac{13}{3}\}$ $\{\frac{13}{4}\}$ $\{\frac{13}{5}\}$ $\{\frac{13}{6}\}$ $\{14\}$ $\{\frac{14}{3}\}$ $\{\frac{14}{5}\}$ $\{15\}$ $\{\frac{15}{2}\}$ $\{\frac{15}{4}\}$ $\{\frac{15}{7}\}$ $\{16\}$ $\{\frac{16}{3}\}$ $\{\frac{16}{5}\}$ $\{\frac{16}{7}\}$ ... $\{\infty\}$ $\{x\}$ $\{\frac{\pi i}{\lambda}\}$
Zerogon Monogon Digon Triangle Square Pentagon Pentagram Hexagon Heptagon Heptagram Great heptagram Octagon Octagram Enneagon Enneagram Great enneagram Decagon Decagram Hendecagon Small hendecagram Hendecagram Great hendecagram Grand hendecagram Dodecagon Dodecagram Tridecagon Small tridecagram Tridecagram Medial tridecagram Great tridecagram Grand tridecagram Tetradecagon Tetradecagram Great tetradecagram Pentadecagon Small pentadecagram Pentadecagram Great pentadecagram Hexadecagon Small hexadecagram Hexadecagram Great hexadecagram ... Apeirogon Failed star polygon ($x$-gon) Pseudogon ($\frac{\pi i}{\lambda}$-gon)
Regular
$t_0 \{10\}$
Rectified
$t_1 \{10\}$
Truncated
$t_{0,1} \{10\}$
Decagon Decagon Icosagon
Regular
$t_0 \{5\}$
Rectified
$t_1 \{5\}$
Truncated
$t_{0,1} \{5\}$
Pentagon Pentagon Decagon

## References

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